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Title: Thermal out-of-time-order correlators, KMS relations, and spectral functions

Abstract

We describe general features of thermal correlation functions in quantum systems, with specific focus on the fluctuation-dissipation type relations implied by the KMS condition. These end up relating correlation functions with different time ordering and thus should naturally be viewed in the larger context of out-of-time-ordered (OTO) observables. In particular, eschewing the standard formulation of KMS relations where thermal periodicity is combined with time-reversal to stay within the purview of Schwinger-Keldysh functional integrals, we show that there is a natural way to phrase them directly in terms of OTO correlators. We use these observations to construct a natural causal basis for thermal n-point functions in terms of fully nested commutators. We provide several general results which can be inferred from cyclic orbits of permutations, and exemplify the abstract results using a quantum oscillator as an explicit example.

Authors:
 [1];  [2];  [2];  [2];  [3]
  1. Univ. of British Columbia, Vancouver, BC (Canada). Dept. of Physics and Astronomy
  2. International Centre for Theoretical Sciences (ICTS-TIFR), Bengahuru (India)
  3. Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)
Publication Date:
Research Org.:
Univ. of California, Davis, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1502422
Grant/Contract Number:  
SC0009999
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Volume: 2017; Journal Issue: 12; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Quantum Dissipative Systems; Stochastic Processes; AdS-CFT Correspondence; Thermal Field Theory

Citation Formats

Haehl, Felix M., Loganayagam, R., Narayan, Prithvi, Nizami, Amin A., and Rangamani, Mukund. Thermal out-of-time-order correlators, KMS relations, and spectral functions. United States: N. p., 2017. Web. doi:10.1007/jhep12(2017)154.
Haehl, Felix M., Loganayagam, R., Narayan, Prithvi, Nizami, Amin A., & Rangamani, Mukund. Thermal out-of-time-order correlators, KMS relations, and spectral functions. United States. doi:10.1007/jhep12(2017)154.
Haehl, Felix M., Loganayagam, R., Narayan, Prithvi, Nizami, Amin A., and Rangamani, Mukund. Fri . "Thermal out-of-time-order correlators, KMS relations, and spectral functions". United States. doi:10.1007/jhep12(2017)154. https://www.osti.gov/servlets/purl/1502422.
@article{osti_1502422,
title = {Thermal out-of-time-order correlators, KMS relations, and spectral functions},
author = {Haehl, Felix M. and Loganayagam, R. and Narayan, Prithvi and Nizami, Amin A. and Rangamani, Mukund},
abstractNote = {We describe general features of thermal correlation functions in quantum systems, with specific focus on the fluctuation-dissipation type relations implied by the KMS condition. These end up relating correlation functions with different time ordering and thus should naturally be viewed in the larger context of out-of-time-ordered (OTO) observables. In particular, eschewing the standard formulation of KMS relations where thermal periodicity is combined with time-reversal to stay within the purview of Schwinger-Keldysh functional integrals, we show that there is a natural way to phrase them directly in terms of OTO correlators. We use these observations to construct a natural causal basis for thermal n-point functions in terms of fully nested commutators. We provide several general results which can be inferred from cyclic orbits of permutations, and exemplify the abstract results using a quantum oscillator as an explicit example.},
doi = {10.1007/jhep12(2017)154},
journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 12,
volume = 2017,
place = {United States},
year = {2017},
month = {12}
}

Journal Article:
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Cited by: 10 works
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Figures / Tables:

Figure 1 Figure 1: A pictorial collection of the various classes of correlators discussed in this section. The green colored boxes denote classes that are useful for generic states. The KMS condition in thermal states introduces a further reduction to the objects collected in blue colored boxes. Generalized uctuation-dissipation theorems (FDTs) describemore » these redundancies. For completeness, note also appendix A, which discusses the relation with standard thermal retarded-advanced Green's functions.« less

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    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.